Mass Spring System

I've got a rather puzzeling question on hand that is part of my Dynamic project. I need to model the collision of two vehicles. Each vehicle is traveling head on to the other, and each one has a spring attached to its front. We can assume that the final velovity after collision is the came for both vehicles. I need to set up an ODE for the system and solve for position vs. time for each vahicle. I have tried this by combining the springs into one spring upon collision but this would not be corrct since the compression of the spring would not give a correct value since there are actually two different springs with fdifferent k's meaning different compressions. If anyone has any help, that would be great.

If you can "assume that the final velovity after collision is the came for both vehicles." then you are really assuming the two vehicles are locked together aren't you? I don't see that you need to set up and ODE. Conservation of momentum should be enough.

If you can "assume that the final velovity after collision is the came for both vehicles." then you are really assuming the two vehicles are locked together aren't you? I don't see that you need to set up and ODE. Conservation of momentum should be enough.

The question strictly states that the motion should be modeled by ODE's and that linear momentum cannot be used (even though in hinsight they are the same).

Either way, I found out that the one spring system can be used, but only to model the CM of each vehicle. It cannot be used to determine the amount that each spring on each car will compress. I have a solution to this compression from another question, so I can use it.